A small weight hangs from a string attached to the rearview mirror of a car acce

Question

A small weight hangs from a string attached to the rearview mirror of a car accelerating at the rate of 1.02 m/s2. What angle does the string make with the vertical?

please expound thanks

Explanation / Answer

From Newton’s 2nd law we find can write an equation for the forces acting horizontally on the weight. The only force acting horizontally on the weight is the horizontal component of tension in the string, so: SF(x) = ma = Tsin?---------------->(1) The forces acting vertically are the vertical component of tension (upward) and the downward weight of the mass: SF(y) = 0 = Tcos? - mg mg = Tcos? T = mg / cos?---------------------->(2) Plugging (2) into (1), we get: ma = (mg / cos?)sin? a = gtan? ? = tan?¹(a / g) = tan?¹(1.02m/s² / 9.80m/s²) = 0.104° Hope this helps.

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